Abstract
The moment’s estimator (Dekkers et al., 1989) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves, 2001) is only suitable to estimate positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type estimator, but is made location invariant by a random shift. Its weak consistency and strong consistency are derived, in a semiparametric setup.
Original language | English |
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Pages (from-to) | 23-31 |
Number of pages | 9 |
Journal | Theory of Probability and Mathematical Statistics |
Volume | 76 |
DOIs | |
Publication status | Published - 2008 |
Externally published | Yes |
Keywords
- Extreme value index
- Location invariant property
- Moment estimation
- Order statistics
- Regular varying functions
- Strong and weak consistencies